THE PRACTICE STUDIO
Go slowly. Ask why. Make it yours.
PRACTICE / Lorentz force
Apply the charge sign last
An electron with q=−1.60×10⁻¹⁹ C enters along +x at 2.0×10⁵ m/s. The electric field is +3.0×10⁴ V/m along y, and B=+0.20 T along z.
What is the initial y component of the total force?
Organize the givens & assumptions
- q=−1.60×10⁻¹⁹ C
- v_x=2.0×10⁵ m/s
- E_y=3.0×10⁴ V/m
- B_z=0.20 T
Uniform perpendicular fields; nonrelativistic point charge; gravity and other forces negligible. The question asks for the initial force only.
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Problem: Apply the charge sign last
An electron with q=−1.60×10⁻¹⁹ C enters along +x at 2.0×10⁵ m/s. The electric field is +3.0×10⁴ V/m along y, and B=+0.20 T along z.
Question: What is the initial y component of the total force?
Givens:
- q=−1.60×10⁻¹⁹ C
- v_x=2.0×10⁵ m/s
- E_y=3.0×10⁴ V/m
- B_z=0.20 T
Assumptions: Uniform perpendicular fields; nonrelativistic point charge; gravity and other forces negligible. The question asks for the initial force only.
Choices (LaTeX):
A. +1.60\times10^{-15}\ \mathrm N
B. -1.60\times10^{-15}\ \mathrm N
C. +1.12\times10^{-14}\ \mathrm N
D. -1.12\times10^{-14}\ \mathrm N
Ask for my approach first. Help me distinguish a physical misconception from an algebra error without revealing which choice is correct.
Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.Start with the smallest hint.
Work through it with me.
One decision at a time. Pause, predict, then unpack the algebra.
The cross product and the sign of the charge are two separate direction decisions.
Resolve the magnetic contribution
The x cross z direction is minus y.
Add the electric contribution
The electric and magnetic terms partly cancel.
Convert field force per charge to force
The negative charge reverses the net direction.
Electric force is −4.8×10⁻¹⁵ N; magnetic force is +6.4×10⁻¹⁵ N.
TRY THE IDEA AGAIN
Reduce the initial speed to 1.0×10⁵ m/s with the same fields. What is F_y?
YOUR LEARNING NOTE
How does this idea feel now?
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